Physical Sciences and Mathematics Commons^™

Mixed Upwinding Covolume Methods On Rectangular Grids For Convection-Diffusion Problems, So-Hsiang Chou, Do Y. Kwak, Panayot S. Vassilevski

Mathematics and Statistics Faculty Publications

We consider an upwinding covolume or control-volume method for a system of rst order PDEs resulting from the mixed formulation of a convection-di usion equation with a variable anisotropic di usion tensor. The system can be used to model the steady state of the transport of a contaminant carried by a °ow. We use the lowest order Raviart{Thomas space and show that the concentration and concentration °ux both converge at one-half order provided that the exact °ux is in H1(­)2 and the exact concentration is in H1(­). Some numerical experiments illustrating the error behavior of the scheme are provided.